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Difficulty: EasyFractions and Decimals

What is the Highest Common Factor (HCF) of the fractions 34\frac{3}{4} and 910\frac{9}{10}?

  1. 320\frac{3}{20}Answer
  2. B
    92\frac{9}{2}
  3. C
    32\frac{3}{2}
  4. D
    920\frac{9}{20}

Answer

The correct Highest Common Factor is 320\frac{3}{20}.
To find the Highest Common Factor (HCF) of a set of fractions, the correct formula is to divide the HCF of their numerators by the LCM of their denominators. For the given fractions, the numerators are 3 and 9, and their HCF is 3. The denominators are 4 and 10, and their LCM is 20. Therefore, the HCF of the two fractions is 320\frac{3}{20}.

Step-by-Step Solution

1
Identify the formula for finding the HCF of fractions.
HCF of fractions = (HCF of Numerators) / (LCM of Denominators)
This is the mathematical rule required to find the greatest common divisor for fractional numbers.
2
Calculate the HCF of the numerators (3 and 9).
The HCF of 3 and 9 is 3.
3 is the largest integer that divides both 3 and 9 without leaving a remainder.
3
Calculate the LCM of the denominators (4 and 10).
The LCM of 4 and 10 is 20.
The multiples of 4 are 4, 8, 12, 16, 20... and the multiples of 10 are 10, 20... The lowest common multiple they share is 20.
4
Divide the result of the numerators' HCF by the denominators' LCM.
320\frac{3}{20}
Applying the values to the formula gives the final fractional answer.

Key Concept

HCF and LCM of Fractions
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Topics

Fractions and Decimals

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